Internship recruiting earlier, but GPA not high enough yet?

How should I time my recruiting?

Almost every major firm seems to be recruiting right now as opposed to the January/February usual, but my GPA is only at a 3.2. I firmly believe I can raise it to a 3.5 after this semester after Excel calculations and very carefully selected classes.

Additionally, I know that it is nearly impossible for me to get an MBB internship right now. What are the best companies to intern for junior year summer if I want to recruit for MBB full-time?

For example, Is getting a tier 2 consulting internship (LEK, Deloitte, etc.) or a brand name F100 internship better for full time MBB recruiting?

Background: semi-target public ivy, quantitative major (not engineering), good leadership + 4 internships

Any guidance is appreciated - thanks in advance!